mysql versions

I'm trying to move my databases to a different server. My original server (local) version is 5.0, but the new server is 4.1.2 and my host says that they cannot restore the database with the dump file i gave them because of this. What's the best way to remedy this?

Would it be possible to download 4.1.2 and move my database to that version and then create a dump file from that server?